build wall wires in way

Hello all. I'm going to be building a closet in my basement in the are in the picture. As you can see, wires are run perpendicular along the joists above in the area where I would place the top plate. I had planned on installing XPS insulation against the concrete wall and then building the back wall. However, the wires are in the way--I was thinking I could tap con a 2x4 to the XPS and into the concrete below the joists and then attach the top plate to that, effectively making a soffit for the wires and any future wires. I could then put XPS and spray foam in the rim joist area. Anyone have any other suggestions--obviously with my method there would be a gap in insulation because it could not run all the way to the ceiling joists.

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Perhaps a little illustration will help. I know its bad but all I have is paint. I would do as shown and then build soffit. Is the gap above the foam board on the wall and the foam board on the rim joist going to create a problem?

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I am wondering about that insulation void you will have. Basically above the wires will be your indoor flooring which shouldn't need insulation aside from the rim joists. The spray from should meet where your XPS Rigid Foam is applied to the concrete wall. Then the gap in the ceiling, or soffit should be open for ventilation and hold your wires in place. Though fishing wires through that small area may prove to be no fun if you do not use something such as 2x2 tiles that can be removed for wiring. Maybe this project should be planned around any other basement renovation you want to do in the future, for example, how you plan on doing the ceiling in other rooms next to this closet?

Thanks for the reply. I'm concerned about the insulation void too. I'm not sure how to get around it. perhaps I can move some of the wires closest to the wall so that I can seal between the insulation in the rim joist areas and the wall insulation.

As far as future access. I was thinking I could put in an access panel as this will just be a closet. I was also thinking I could mount a piece of 2" PVC conduit in the soffit so that I could pull any future necessary wires through that.

Lastly, there is an area in front of this closet (future hallway) that does not have a ceiling yet, where I could run future wires if necessary (before I eventually finish that)